Deep Inverse Optimization
This work addresses the challenge of parameter estimation in optimization models for researchers and practitioners, representing a novel integration of deep learning with optimization but is incremental in applying existing deep learning techniques to a specific domain.
The paper tackles the problem of inferring optimization process parameters from observed solutions by framing inverse optimization as a deep learning task, using backpropagation through unrolled iterative algorithms to learn cost vectors and constraints for linear programs, achieving results that enable parameter learning from single or multiple observations.
Given a set of observations generated by an optimization process, the goal of inverse optimization is to determine likely parameters of that process. We cast inverse optimization as a form of deep learning. Our method, called deep inverse optimization, is to unroll an iterative optimization process and then use backpropagation to learn parameters that generate the observations. We demonstrate that by backpropagating through the interior point algorithm we can learn the coefficients determining the cost vector and the constraints, independently or jointly, for both non-parametric and parametric linear programs, starting from one or multiple observations. With this approach, inverse optimization can leverage concepts and algorithms from deep learning.